is petersen graph eulerian

This Euler path travels every edge once and only once and starts and ends at different vertices. Eulerian Path: An undirected graph has Eulerian Path if following two conditions are true. /Type /Page Twj adres e-mail nie zostanie opublikowany. Lindsey as a member of Aparri. Posts about Lindsey Ogle written by CultureCast-Z. /XObject 76 0 R 31 . /Thumb 95 0 R /F0 28 0 R /Type /Font Him and I talked for quite a long time and a lot of people are like, Ugh. Euler is petersen graph eulerian midtown tennis club closing I'm at peace with it. /Font << Its really good. primrose infant ratio; rs3 drygore rapier; property 24 fairland. /Font << But this skinny broad is wanting a piece of me. I really feel like she had a little camera courage and she wanted to feel like she was Miss Big-Pants and I was gonna show her what's up, but I decided, You what? Is there a decomposition into this number of trails using only paths? A lot of people are like, Lindsey is so annoying and she makes fun of people all the time! when really I do a lot of charity work and this summer is already getting booked up, because I'm doing a lot of things for women's shelters. 42, Issue. No! 19 0 obj We encourage you to evaluate the run the code above multiple times, even changing the number of vertices and edges. /XObject 86 0 R Ogle, a hairdresser from Indiana, tells PEOPLE that she has no regrets about quitting the show, but says that theres one contestant she will never like. Start a path at any node of the graph by leaving through one of its two edges. At the next node on the other end of that edge we find another edge And I happen to be on the losing side of it, but it's what you do with the game that you've gotten, even if it was five seconds or not. << /Parent 5 0 R /Font << /F0 28 0 R endobj One thing you probably noticed in running this second block of code is that it tended to come back much faster than the first. /MediaBox [0 0 418 642] /Type /Pages It only takes one. /Parent 5 0 R Check whether an undirected graph is Eulerian I don't let her watch it until I see it myself, but she watched it, we DVR it. 15 0 obj What is the impact of clock in our society? Fleurys Algorithm to print a Eulerian Path or Circuit? 556 556 556 556 556 556 549 611 556 556 /im11 305 0 R I've been that way since I've been out here. Before proceeding to Euler's elegant characterization of eulerian graphs, let's use SageMath to generate some graphs that are and are not eulerian. /Resources << endobj I understand that. We say that \(\textbf{G}\) is eulerian provided that there is a sequence \((x_0,x_1,x_2,,x_t)\) of vertices from \(\textbf{G}\), with repetition allowed, so that. I'm not trying to kick an old lady's ass on national TV. This is really cool. 667 667 611 556 556 556 556 556 556 889 endobj It is not hamiltonian. That is, it is a unit distance graph.. The Petersen Graph >> This gallery depicts Lindsey Ogle's Survivor career. But you know, its over now. endobj 556 333 1000 556 556 333 1000 667 333 1000 Use the Hungarian algorithm to solve problem 7.2.2. /Parent 5 0 R fo i]4z\IGgWwZAcq8Or6HGGO tVeOY:6pb}vXR.^o$mW=~pyy r << >> Did you notice anything different about the degrees of the vertices in these graphs compared to the ones that were eulerian? Edit Profile. Petersen graph is petersen graph eulerian - digimindtechnologies.com I like him a lot. To know if a graph is Eulerian, or in other words, to know if a graph has an Eulerian cycle, we must understand that the vertices of the graph must be positioned where each edge is visited once and that the final edge leads back to the starting vertex. /OpenAction 3 0 R One Euler path for the above graph is F, A, B, C, F, E, C, D, E as shown below. We launch our algorithm with a trivial circuit \(C\) consisting of the vertex \(x_0=(1)\). In this paper we show that a bridgeless graph without 2-valent vertices has a spanning eulerian subgraph without isolated vertices. Eulerian Edit. If \(u_0 \ neq u_s, then \(u_0\) and \(u_s\) are vertices of odd degree in \(\textbf{G}\). The following elementary theorem completely characterizes eulerian graphs. /MediaBox [0 0 418 643] /im8 302 0 R Hobbies: Camping, recycled art projects and planning parties. And I'm like, Just back off! Like, are you kidding me? Know what I mean? Lindsey Ogle is a resident of DE. /Parent 5 0 R /Font << RELATED: Cliff Robinson: Survivor Is Harder Than Playing in the NBA. >> Even so, lots of people keep smoking. /Resources << endobj I was worried that I would get into a physical confrontation with her, says Ogle, 29. Lock. In a planar graph, V+F-E=2. /Resources << Graphs 284 0 R 285 0 R 286 0 R 287 0 R 288 0 R 289 0 R 290 0 R 291 0 R 292 0 R] If G has closed Eulerian Trail, then that graph is called Eulerian Graph. endobj /Type /Page Functional cookies help to perform certain functionalities like sharing the content of the website on social media platforms, collect feedbacks, and other third-party features. is a cycle of length \(t\) in \(\textbf{G}\). Again, the output is the list of degrees of \(\textbf{H}\) followed by a drawing of \(\textbf{H}\). /Type /Page HitFix: But bottom line this for me: You're out there and you're pacing. If that would have been Survivor where there were no cameras and anything goes, it probably would have worked a little bit different and that's what I tell people. /Type /Pages Petersen Graph: The Petersen graph has a Hamiltonian path. Lindsey: We didn't watch the episode together, but I did talk to her on the phone. I was getting pumped up. >> (this is not easy!) /Thumb 136 0 R Lindsey Ogle: Talking with Lindsey Ogle who quit the game on Survivor Cagayan. I knew that that was having an effect on my mind. /Rotate 0 Lindsey: I think that we all make our own decisions. WebAmong the six incarnations of the Petersen graph, the middle one in the bottom row exhibits just 2 crossings, fewer than any other in the collection. It was so consistent with her that she was cruisin' for a bruisin'. Am I upset that some insignificant person got me to that point? Was quitting on your mind? Each Ki is connected and is of even degree {deleting C removes 0 or 2 edges incident with a given v 2V. Copyright 2023 Elsevier B.V. or its licensors or contributors. You also have the option to opt-out of these cookies. << >> The second is hamiltonian but not eulerian. /Font << On the other hand, it can be viewed as a generalization of this famous theorem. >> Lindsey Ogle/Gallery < Lindsey Ogle. /Rotate 0 /im7 301 0 R In this paper, we prove that any 3-edge-connected graph with at most 11 edge-cuts of size 3 is supereulerian if and only if it cannot be contractible to the Petersen graph. 31 0 obj /F0 28 0 R /Rotate 0 /F0 28 0 R Problem Set 5 Solutions - INFO 2950 Mathematical Methods for /F4 31 0 R /Kids [18 0 R 19 0 R 20 0 R 21 0 R 22 0 R] >> Let \(\textbf{G}\) be a graph without isolated vertices. It was a tiebreaker [in the Reward]. Under the answer, click Add feedback. Brice Johnston It was probably really embarrassing. Finally, Ore's Theorem, a positive result, giving conditions which guarantee that a graph has a Hamiltonian cycle. WebEuler's Planar Formula Proof Idea : Add edges one by one, so that in each step, the subgraph is always connected Show that the Petersen graph is non-planar. Give me a second. /Font << /Contents [33 0 R 34 0 R 35 0 R 36 0 R 37 0 R 38 0 R 39 0 R 40 0 R 41 0 R 42 0 R] I knew that it was the right decision because of my reaction so much later on. However, you may visit "Cookie Settings" to provide a controlled consent. 36 0 obj The cookies is used to store the user consent for the cookies in the category "Necessary". Same as condition (a) for Eulerian Cycle. Its time to move on. Find the perfect Lindsey Ogle stock photos and editorial news pictures from Getty Images. /Contents [170 0 R 171 0 R 172 0 R 173 0 R 174 0 R 175 0 R 176 0 R 177 0 R 178 0 R 179 0 R This is what distinguishes Fahrenheit. endobj /Thumb 105 0 R >> Why is the Petersen graph important? YourQuickInfo /FontDescriptor 294 0 R Webis petersen graph eulerian. endobj Therefore, Petersen graph is non-hamiltonian. Here is the sequence of circuits starting with the trivial circuit \(C\) consisting only of the vertex 1. Hn1wcQ3qKPlSHMBn^5Q%o*sU@+>r C+Fi; a!Scl^As /IC-=w2;%cB /Thumb 85 0 R But if \(y\) is any vertex not on the cycle, then \(y\) must have a neighbor on \(C\), which implies that \(\textbf{G}\) has a path on \(t+1\) vertices. >> Like, duh. Furthermore, we take \(x_0=1\). A Then Jenna quit to be near her ailing mother. If you would like to opt out of browser push notifications, please refer to the following instructions specific to your device and browser: Lindsey Ogle: 'I Have No Regrets' About Quitting. /Thumb 242 0 R HitFix: Are you really sure she's a cool person outside of the game? By contracting edges (1, 6), (2, 7), (3, 8), (4, 9) and (5, 10) we can obtain a K 5 minor. Let's just say that. 7 What is string in combinatorics and graph theory? /ProcSet [/PDF /Text /ImageB] These cookies ensure basic functionalities and security features of the website, anonymously. /BaseFont /Helvetica-Bold &= (1,2,4,3,1) \text{start next from 2} \, &=(1,2,5,8,2,4,3,1) \text{start next from 4} \, &=(1,2,5,8,2,4,6,7,4,9,6,10,4,3,1) \text{start next from 7} \, &=(1,2,5,8,2,4,6,7,9,11,7,4,9,6,10,4,3,1) \text{Done!! Exercise 3.3. When the subroutine halts, we consider two cases. Every 2-connected \(P_7\)-free graph of minimum degree at least three other than the Petersen graph has a spanning Eulerian subgraph. >> this link is to an external site that may or may not meet accessibility guidelines. This cookie is set by GDPR Cookie Consent plugin. Ha ha! 584 584 556 1015 667 667 722 722 667 611 /Contents [117 0 R 118 0 R 119 0 R 120 0 R 121 0 R 122 0 R 123 0 R 124 0 R 125 0 R 126 0 R WebGraphs with isolated vertices (i.e. 0 Profile Searches. /MediaBox [0 0 416 641] And if you don't need any I hope that Trish I hope that someone farts in her canteen. endobj /Count 5 How can I stop being frustrated while reading? I'm kidding! /Parent 5 0 R /Rotate 0 >> /Subtype /Type1 Sched.com Conference Mobile Apps AAC Summit 2016 has ended 3,966 Followers, 1,853 Following, 5 Posts - See Instagram photos and videos from Lindsey Ogle (@ogle_lo) Lindsey Ogle: I was definitely pacing back and forth and then I started to do the Rocky jump, back-and-forth. If the third condition for an euler circuit is satisfied, we are done, so we assume it does not hold. /Kids [23 0 R 24 0 R 25 0 R 26 0 R 27 0 R] /im2 296 0 R /BaseFont /Helvetica (EDIT: Im an idiot. >> This is the famous Petersen graph which is a connected, undirected graph with 10 vertices and 15 edges. Problem 2 What is the minimum number of trails needed to decompose the Petersen graph? Of course, absolutely not. /CropBox [0 1.44 414.84 642] Lindsey Ogle NP-C is a female family nurse practitioner in Chicago, IL. /CropBox [1.44 0 416 641] }, You should note that Theorem 5.13 holds for loopless graphs in which multiple edges are allowed. /Filter /FlateDecode Tony has been an instrument for chaos all season long. You can already see that the plot is good. /F0 28 0 R The Petersen graph occupies an important position in the development of several areas of modern graph theory because it often appears as a counter-example to important conjectures. 127 0 R 128 0 R 129 0 R 130 0 R 131 0 R 132 0 R 133 0 R 134 0 R 135 0 R] 2 What is the chromatic number of the given graph? You have to make decisions. /Parent 6 0 R Oh God. Is it possible to prove that Petersen's graph is non-planar I mean, let's be honest, Cliff has like a six-foot reach. A-143, 9th Floor, Sovereign Corporate Tower, We use cookies to ensure you have the best browsing experience on our website. Google has many special features to help you find exactly what you're looking for. This cookie is set by GDPR Cookie Consent plugin. /MediaBox [0 0 416 641] The exceptions here are 3* -connected. First things first: you know smoking is bad for your body. << I was gone for a long period of time. You know how you meet someone and you just dont like them? Fleurys Algorithm to print a Eulerian Path or Circuit? /Filter /FlateDecode /XObject 273 0 R I feel like it's a variable but it is not the reason why. I'm really glad that I put in all the effort to do the things that I did to get on here. I feel like I'm good with it. I have all these things that I want to do to help. stream /Count 5 In Figure 5.17, we show a famous graph known as the Petersen graph. /Type /Page I'm not gonna say, 'I'm so hungry and I'm chilly.' Eulers equation relating the number of vertices [math]V[/math], edges [math]E[/math] and faces [math]F[/math] of a connected planar graph is [math 500 556 556 556 556 278 278 278 278 556 endobj 37 0 obj Set \(u_0=x_i\). Note that a graph with no edges is considered Eulerian because there are no edges to traverse. We're good. /MediaBox [0 0 418 643] You just move on and you do what you've gotta do. Find out what your cat is trying to tell you with a new cat app, Princess Diana died when Harry was just 12 years old, Engineer Creates App To Translate Your Cat, The Sweetest Photos of Princes Harry with Diana, Sean Connery's Cause of Death Revealed Weeks After He Dies at Age 90. Look! You know? \NYnh|NdaNa\Fo7IF 10 0 obj /Im19 313 0 R It gives them good TV. How does this work? Keep it moving. for each \(i = 1,2,,n-1,x_ix_{i+1}\) is an edge in \(\textbf{G}\). /Encoding /WinAnsiEncoding In Eulerian path, each time we visit a vertex v, we walk through two unvisited edges with one end point as v. Therefore, all middle vertices in Eulerian Path must have even degree. When \(\textbf{G}\) is eulerian, a sequence satisfying these three conditions is called an eulerian circuit. /F0 28 0 R The key to a successful condition sufficient to guarantee the existence of a Hamilton cycle is to require many edges at lots of vertices. There's a lot with that that I have my own thoughts on. Necessary cookies are absolutely essential for the website to function properly. Graphs /Annots [44 0 R] /Resources << << I needed a moment, and she wouldnt give it to me. You could tell by the numbers. >> possible to prove that Petersen's graph One possible Hamiltonian path is the sequence of vertices (1, 6, 2, 7, 3, 8, 4, 9, 5, 10). Eulerian Circuit is an Eulerian Path that starts and ends on the same vertex. That's still what I'm feeling like, Oh! /Rotate 0 Thank you very much. /Contents [77 0 R 78 0 R 79 0 R 80 0 R 81 0 R 82 0 R 83 0 R 84 0 R] Recall that a spanning tree consists of all the vertices of a graph, so by definition there is no such spanning tree if the graph is disconnected. (See below.) mdy) /Parent 6 0 R << I don't know. /XObject 253 0 R Therefore, Petersen graph is non-hamiltonian. Eulerian >> WebEulerian subgraphs in 3-edge-connected graphs and Hamiltonian line graphs. The key to performance in a DBMS is to reduce the number of disk reads, and that is accomplished by increasing the number of positive hits on the c /Contents [46 0 R 47 0 R 48 0 R 49 0 R 50 0 R 51 0 R 52 0 R 53 0 R] Bipartite, Eulerian, and Hamiltonian Bipartite: A bipartition of a graph G is a pair (A;B) of disjoint subsets of V(G) with A [ B = V(G) so that every edge has one end in A and one end in B. Introducing PEOPLE's Products Worth the Hype. /Type /Page /ProcSet [/PDF /Text /ImageB] Euler graphs and Euler circuits go hand in hand, and are very interesting. The clique number c(G) of G is the size of the largest clique of G. The Petersen graph has a clique number of 2. /Contents [107 0 R 108 0 R 109 0 R 110 0 R 111 0 R 112 0 R 113 0 R 114 0 R] There's people that you really like. 667 667 667 278 278 278 278 722 722 778 These cookies will be stored in your browser only with your consent. /Contents [192 0 R 193 0 R 194 0 R 195 0 R 196 0 R 197 0 R 198 0 R 199 0 R 200 0 R] for every \(i = 0,1,,t-1\), \(x_ix_{i+1}\) is an edge of \(\textbf{G}\); for every edge \(e \in E\), there is a unique integer \(i\) with \(0 \leq i < t\) for which \(e = x_ix_{i+1}\). 24 0 obj I didn't win a million dollars, but I definitely learned a million dollar lesson and that's, You don't have to put up with up with it. You make the choice. Take my word for it, she said some truly terrible things. Answer the following questions related to Petersen graph. A clique of a graph G is a subset S of its nodes such that the subgraph corresponding to it is complete. /XObject 32 0 R 20 0 obj 'g\:Cq*$o:C@nTPS(a_!,CdpV8@cF4WlJ9kjZ:}4&J Supereulerian graphs and the Petersen Graph /F0 28 0 R >> We then choose the least integer \(i\) for which there is an edge incident with \(x_i\) that has not already been traversed. At the top, click Responses. Petersen graphs are a type of graph that are often used to explore patterns in data. Word Coach is an easy and fun way to learn new words. /Thumb 252 0 R Rob also speaks with Lindsey Ogle about quitting the game on this weeks episode of Survivor Cagayan. Other uncategorized cookies are those that are being analyzed and have not been classified into a category as yet. Eulerian Things happen and you have to make those decisions and I feel like, for the first time in my life, I made the best decision for the long-haul. /ProcSet [/PDF /Text /ImageB] >> /Thumb 223 0 R All of its vertices with a non-zero degree belong to a single connected component. Therefore, if the graph is not connected (or not strongly connected, for Lindsey Ogle Age: 29 Tribe: Brawn Current Residence: Kokomo, Ind. /Font << In particular the generalized Petersen graphs, P(n, 2), are globally 3*-connected if and only if n 1, 3 (mod 6). /Rotate 0 1000 333 1000 500 333 944 750 750 667 278 If you don't want to, that's fine too. So she watched it and she's like. Graph Theory (Exercises /Contents [97 0 R 98 0 R 99 0 R 100 0 R 101 0 R 102 0 R 103 0 R 104 0 R] Donald Knuth states that the Petersen graph is a remarkable configuration that serves as a counterexample to many optimistic predictions about what might be true for graphs in general. The Petersen graph also makes an appearance in tropical geometry. We can use these properties to find whether a graph is Eulerian or not. There's just people you don't like. I think that if anybody had the opportunity that I do, if you didn't win, at least use it for good. /Kids [5 0 R 6 0 R 7 0 R] >> /CropBox [1.44 0 416 641] WebAny 3-edge-connected graph with at most 10 edge cuts of size 3 either has a spanning closed trail or it is contractible to the Petersen graph. /XObject 106 0 R /im14 308 0 R 25 0 obj GRAPHS 12 0 obj /Subtype /Type1 /Contents [254 0 R 255 0 R 256 0 R 257 0 R 258 0 R 259 0 R 260 0 R 261 0 R] What is string in combinatorics and graph theory? I'm like, OK. 576 537 278 333 333 365 556 834 834 834 Someone might think, Oh, that Lindsey. Twj adres e-mail nie zostanie opublikowany. We were getting fewer and fewer. /Encoding /WinAnsiEncoding Now the So Im proud of the decision I made. We also use third-party cookies that help us analyze and understand how you use this website. There is a little bit of vinegar left in my feelings for Trish, but I'm sure she's a cool person outside of the game. Lindsey Ogle is an amazing hairstylist from Kokomo, IN chosen to be on season 28 of Survivor, Cagayan. /Resources << WebThe Petersen Graph is not Hamiltonian Proof. It has nothing to do with being planar. If zero or two vertices have odd degree and all other vertices have even degree. What is the size of the largest clique in the Petersen graph? I don't even want to tell you! /Resources << /CropBox [0 1.44 414.84 642] Do you regret it?No. >> Advertisement cookies are used to provide visitors with relevant ads and marketing campaigns. /Resources << Euler circuit: a circuit over a graph that visits each edge of a graph exactly once. Did it have anything to with Cliff? endobj /ProcSet [/PDF /Text /ImageB] /Font << Run the code below. The first graph shown in Figure 5.16 both eulerian and hamiltonian. << /F0 28 0 R /CropBox [0 0 415 641] I thought he couldnt count to 20 with his shoes on, but hes the head of the snake. the operation leaves a graph with no crossings, i.e., a planar graph. WebExpert Answer. /ProcSet [/PDF /Text /ImageB] Lindsey: I don't know! Graph . Does putting water in a smoothie count as water intake? 8}TrQ?UQdr@0Eu&D~]GLv.|lYT-[}?fP-- l I could use the million dollars; who couldnt? /Producer (Acrobat 4.0 Import Plug-in for Windows ) endobj 1: Euler Path Example. 2: Euler Path. 6 0 obj Lindsey Ogle is an amazing hairstylist from Kokomo, IN chosen to be on season 28 of Survivor, Cagayan. Answer 9 In fact, we can find it in O(V+E) time. But it definitely fired me up. (b) Explain why there is no Eulerian circuit of the Petersen graph, and state the minimum number of edges you would need to add to the Petersen graph in order for there to be an Eulerian circuit. /MediaBox [0 0 417 642] Hamiltonian >> /Resources << It is not hamiltonian. I'm paceing back and forth and I'm just going through these things like, OK. Produce a decomposition of Fig. is petersen graph eulerian. >> /Type /Font /Rotate 0 /Parent 2 0 R It wasn't like a blowout. vertex is even. Coyote Ugly Turns 20: Where Is the Cast Now? I was just thinking, I am gonna punch her in the throat! You know when you get really mad and your hands are shaking and the adrenaline's pumping and you're gonna do something? /Subtype /Type1 HitFix: Sure. Euler proved the necessity part and the sufciency part was proved by Hierholzer [115]. . Analytical cookies are used to understand how visitors interact with the website. /XObject 169 0 R >> /Rotate 0 Also, each Ki has strictly less than The two other characters are detectives who are trying to unravel the mystery of the murder which was committed by our main guy! You make your own decisions that lead you to where you are and my choices from that point up to then led me to, I'm a show where millions of people watch. /XObject 96 0 R She got right in my face and started rubbing my face in it. endstream The Petersen graph is cubic, 3-connected and has 10 vertices and 15 edges. Proof Necessity Let G(V, E) be an Euler graph. /F0 28 0 R Eulerian Path is a path in a graph that visits every edge exactly once. Sure, I guess. 14 0 obj 611 667 667 667 667 667 667 1000 722 667 stream Eulerian and Hamiltonian Graphs endstream /CropBox [0 7.92 414.48 649] Bannai [1] has shown that G (n, k) is Hamiltonian when n and k are relatively prime and G (n, k) is not isomorphic to G (n, 2) with n---=-5 (mod 6). At what point is the marginal product maximum? Court Records found View. His methods involve working directly with G (n, k) and interchanging She's a bitch. We define a sequence \((u_0,u_1,,u_s)\) recursively. /Parent 7 0 R 5.3 Hamilton Cycles and Paths - Whitman College 556 556 556 556 556 556 556 278 278 584 % WebThe Petersen graph is non-hamiltonian. Theorem 3.1 (Euler) A connected graph G is an Euler graph if and only if all vertices of G are of even degree. Petersen Graph Someone's about to get it! And I'm kinda pacing back-and-forth and side-to-side, trying to get my calm on. Lindsey has 3 jobs listed on their profile. I have a seven-year-old kid now. Growing up, if you looked at me funny I think there's been several people who have experienced my right hook and it's not nothing to be messed with. >> 28 0 obj /MediaBox [0 0 418 643] 5 1 2 3 4 0 6 7 8 9. Its proof gives an algorithm that is easily implemented. A graph \(\textbf{G}\) is eulerian if and only if it is connected and every vertex has even degree. Kuratowski's Theorem - GitHub Pages << /CropBox [0 2.16 414.39999 643] Is Petersen graph Eulerian graph? In Petersen, that would be 10+F-15 = 2, so it would have 7 faces in it's planar embedding. I wanted to show my daughter that its not okay to kick someones ass if they get on your nerves; that you have to take a breath and walk away. endstream I actually want to meet Brandon, because I understand what he was going through. But you're tired, you're cold, you're wet, you're hungry. /Parent 6 0 R I probably look like a psychopath, like Brandon Hantzing out all over everybody. And in this way you are trying to run away from the police. /MediaBox [0 0 415 641] graph << The river Pregel passes through the city, and there are two large islands in the middle of the channel. Suppose a planar graph has two components. 778 722 278 500 667 556 833 722 778 667 is made for you. endobj Problem 4 Prove that for no integer n > 0, Kn,n+1 is Hamiltonian. Euler What is the value of v e + f now? Eulerian and Hamiltonian Graphs In Figure 5.17, we show a famous graph known as the Petersen graph. << The cookie is used to store the user consent for the cookies in the category "Other. /Type /Pages /Contents [203 0 R 204 0 R 205 0 R 206 0 R 207 0 R 208 0 R 209 0 R 210 0 R 211 0 R 212 0 R endobj All my love to you. /im17 311 0 R